A relativistic electron-positron pair beam can be produced in the interaction between TeV photons from a blazar and extragalactic background light. The relativistic e(+/-) pairs lose energy through inverse-Compton scattering (ICS) photons of the cosmic microwave background or plasma instabilities. The dominant energy-loss process is under debate. Based on the assumption that the dominant energy-loss process is ICS, the resulting cascade GeV radiation is usually used to constrain the intergalactic magnetic field (IGMF). Here, we include the energy-loss due to plasma oblique instability in the calculation of cascade gamma-ray flux, and investigate the impact of the plasma instability on the constraint of IGMF. Up-to-date GeV data and archival TeV data of the blazar 1ES 0229+ 200 are used. The results indicate that even if the oblique instability cooling is dominating ICS cooling, the cascade flux could still be used to constrain the IGMF. It is found that with the ratio between the cooling rates of the oblique instability and the ICS varying from 0.1,1 to 10, the lower limit of the IGMF of the cascade flux and the gamma-ray data changes from 8 x 10(-1)8 G, 5 x 10(-18) G to 10(-18) G. If the ratio between the two cooling rates is 30, the estimate of IGMF based on the cascade flux is invalid.